Control network



Aug. 19, 1947.

E. L. HARDER `2,426,018

CONTROL NETWORK Filed 001'.. 25, 1944 www ATTORN EY Patented Aug. 19, 194'? CONTROL NETWORK Edwin L. Harder, Forest Hills, Pa., assigner to Westinghouse Electric Corporation, East Pittsburgh, Pa., a corporation of Delaware Application October 25, 1944, Serial No. 560,299

21 Claims.

My invention relates to new and highly eicient networks for obtaining positive or negative-sequence voltages.

An object of my invention is to provide a compensator-type network or combination, for deriving a positive-sequence Voltage from a single phase of a three-phase line-voltage having no zero-sequence voltage-component, minus a compensator-voltage which is derived by passing linecurrent through impedance in such manner as to produce a voltage-drop equal to the negative-sequence voltage-component. This positive-sequence network or combination is particularly useful in a system in which the load on the positive-sequence terminals of the network is variable, and in which it is important to reduce the variation of the derived positive-sequence voltage at the load-terminals, when said load varies between zero and full-load. An example of .such a variable positive-sequence load is a voltage-regulator of a type having a network consisting of various variable shunt-loads, connected -by a serially-connected impedance, and all energized from the positive-sequence output-terminals of the positivesequence network.

A still further object of my invention is to provide a current-compensator type of means, for deriving the negative-sequence component of a line-voltage, by causing a plurality of impedances to `be traversed by two phases of a three-phase linecurrent, either delta or star or other type of current, the currents being either currents having no zero-sequence component or currents from which the zero-sequence component has been removed, and the impedances being so chosen as t produce substantially the same impedance-drop as is obtained by passing the negative-sequence line current through the negative-sequence impedance of the line up to the point at which the negative-sequence voltage is to be measured or derived.

With the foregoing and other objects in view, my invention consists in the circuits, systems, combinations, apparatus, parts, and methods hereinafter described and claimed, and illustrated in the accompanying drawing, wherein Figs. 1 to 7 are diagrammatic views of circuits and apparatus comprising different illustrative forms of embodiments of a positive-sequence network or combination embodying my invention, and Fig. 8 is a still more diagrammatic view of a voltage-regulator system utilizing my invention, by which I mean a system in which the positive-sequence network feeds into a variable load, under conditions in which it is important to consider the variation of the derived voltage at the load-terminals, when the load of the voltage-regulator varies between zero and full-load. Y

In Fig. 1, I have indicated a system in which the voltage of a three-phase line A, B, C is to be determined at some point l. The particular line which is illustrated is energized by a polyphase generator G through a delta-star power-transformer T. I provide a potential-transformer P'Iab for deriving the delta-voltage Eab from the line-conductors A and B. I also provide two linecurrent transformers CTE and C'Ic for deriving the star-phase line-currents Ia and Ic, from the line-conductors A and C, respectively. I also provide certain impedances which will subsequently be described.

The phase-A and phase-B star-voltages of the line, in terms of the star-voltage phase-sequence components Eo, E1 and E2, are

Hence the phase-AB delta-voltage is From this it follows that the positive-sequence delta-voltage is :Eat-Ecm :Eat-(l-wEz (4) The negative-sequence star-voltage E2 is E2=-I2(R2+7`X2) (5) where I2 is the negative-sequence star-current and (Rza-7X2) is the negative-sequence impedance of the generator G and the transformer T, or, in general, the combined generator-and-line negative-sequence impedance up to the point at which the voltage is measured.

The negative-sequence current is Hence, from Equations 6 and 8, the negative-sequence star-current is 3 I2=1/3(Ialc/,2Iblalc) #1/3(1+a2 a)1o 1/3[ Ia-Io) a2(It-I0) a c lo)l (9) By combining Equations l and 9, any one of the three currents (Ia-Jo), (Ib-Jo), or (Icvlo) may be eliminated. Thus, from Equation "I,

(Ib-I) =-(Ia-Io) (16-10) (10) which, substituted in Equation 9, gives the value of the negative-sequence star-current as I2=1;[(1-a2) (Ia-Io) -l-(a-a2l (Ic-10U (11) Combining Equations 4, 5 and 11 shows that the positive-sequence delta-voltage is Eab1=Eab+ (1 0) (R2-MK2) I2 (12) =Eab+1/3(1 a) (Rz-l-y'Xz) [(1 a2) (1a10 -l- (rz-a2) (Ic-I0] =Eab-{(R2+7`X2) [Ua-J0) -cWIc-Io) l :Eat RMLL In) -ly'XzUa 10) (1/2\/3X2 1/R2) (In Io)'r+7'(1/2X2 -l- 1/p v\/R2)(Ic- In) (13) Instead of eliminating the current (It-I0) from Equations 9 and 10, we could have eliminated (Ia-Jo) or (Ic-Io), yielding I2=-1/3[(1 a2) (It-I0)l(1a) (h .oll (11') I2=1/3l(1a) (IV-Io) m2-a) (It-Iol l whence Instead of starting out with the delta-voltage in phase-AB, we could have taken either of the By relettering the phases, and calling them C, A, B instead of A, B, C, Equations 13h, 13b and 13b become identical with Equations 13', 13 and 13, respectively. By relettering the phases, and calling them B, C, A instead of A, B, C, Equations 13C, 13C' and 13o" become identical with Equations 13, 13 and 135, respectively. We will coniine our attention, therefore, to Equations 13, 13 and 13, as the fundamental equations for star line-currents Ia, Ib and Ic.

Equation 13 states that the positive-sequence delta-voltage may be obtained by passing the current (Ia-Io) through an impedance (R2-MK2), and passing the reversed current UV-Io) through an impedance and by adding the two impedance-drops to the delta line-voltage Eat. Or the reversed current UC-In) may be passed through a resistance having a value (12V3X2-1/2R2), and the unreversed current (Ic-In) may be passed through an inductive reactance j/gXz-l-lgvlg). Or the currents may be doubled and the impedances halved, or vice versa, etc. Actually, of course, as is well-known in relaying practice, when currenttransformers CT and potential-transformers PT are used, the secondary ohms used for R2 and X2 must be the CT-ratio, divided by the PT-ratio, times the actual primary ohmic value of R2 and X2. It is usually more convenient to express the negative-sequence line-impedance (Rz-HXQ) as a percentage of the line-v0ltage at the full load (EL) line-current at the rated load of the generator.

Equation 13 States that the positive-sequence delta-voltage may be obtained by passing the reversed current Ut- 10) through an impedance (Rz-l-jXz), and passing the reversed current (10-10) through an impedance and by adding the two impedancedrops to the delta line -voltage Eat.

Equation 13 states that the positive-sequence delta-voltage may be obtained by passing the current (Ia-I0) through an impedance and passing the current (It-I0) through an irnpedance and by adding the two impedance-drops to the delta line-voltage Eat.

The three currents3 (Ia-It), (Ib-I0) and (ICI0) are the line-currents Ia, Ib and Ic from which the Zero-sequence component has been removed. There are several means, Well-known in the art, for deriving the line-currents less the Zero-sequence components, and these means form no essential part of my invention. For convenience in illustration and description, I shall, therefore, illustrate rmy invention as being applied to a system in which there is no zerosequence current, or 10:0. Thus, in Fig. 1, neither the generator G nor the power-transformer T is grounded, and hence Iu=0.

In many cases, the resistance-componentl Rz is negligibly small,.in the negative-sequence lineimpedance (R2+iX2) from the internal voltage of the generator G up to the pointat lwhich the line-voltage is to be measured. For simplicity of illustration, I shall therefore illustrate my invention as being applied to a system in which R2=0, within the required limits of accuracy, with the understanding that the quantity Rz may be taken into consideration, if necessary, in the manner indicated by the Equations i3, 13 or 13".

The negative-sequence impedance 7X2 may have any value. By way of concrete illustration, I shall assume that X2 is a 25% reactance, that the secondary voltage of the potential-transformer PTab is 115 volts, and that the secondary current, in the seco-ndary windings of the current-transformers CTa and CTC is i amperes at full load on the generator. Then the secondary impedance, corresponding to 100% line-impedance, will be 115/4=28.75 ohms, and the ohmic value of the negative-sequence impedance X2, to be used in the secondary circuit, is

0.25 28.75=7.19 ohms Thus, in Fig. 1, I may provide a secondaryresistor having a value 1/2 @X2 or essere shunted by a transformer Tr having a ratio 1:1. Or the resistor might have been 8.661212 and the transformer-ratio :1, etc. This resistor is connected in circuit with the secondary current Ic of the current-transformer CTe, so as to produce a secondary potential 6.866X2I2 as required by the fourth term of the right-hand side of Equation 1S. Polarity-marks, fr, indicate the relative instantaneous polarities in the usual manner.

In Fig. 1, I also provide a three-winding mutual inductance having two primary windings Wa and We and a secondary winding Ws, with a mutual reactance 7X2 between Wa and Ws, and a mutual reactance y' 1/2X2 between We and Ws, as indicated. The primary windings Wa and We are respectively connected in circuit with the secondary currents Ia and Ie of the currenttransformers C'I's and CTC, respectively, and the secondary winding Ws is connected in series with the secondary circuit of the resistance-shunting transformer Tr, in the secondary circuit J of the potential-transformer PTab.

Thus, in the operation of the voltage-deriving network shown in Fig. l, the potential-transformer PTab produces the secondary delta-voltage Eat, and the resistance-shunting transformer Tr and the reactor-secondary Ws together produce the secondary negative-sequence voltage which is subtracted from the delta-voltage Eat to produce the positive-sequence voltage Essi, as indicated in Fig. l, and in conformity with Equation 13, still assuming a System in which I0=0 and 122:0.

In Fig. 2, a similar positive-sequence voltagecircuit is shown, in which current-transformers CTB. and CTb are utilized in line-phases A and B, instead of phases A and C as in Fig. 1. In Fig. 2, the phase-C current is obtained from the relation enrichie as indicated by the arrow Ic in Fig, 2". The powertransformer T of Fig. 1 is not used in Fig. 2. Fig. 2 is otherwise the same as Fig. 1, and the operation is the same.

In Fig. 3, no potential transformer is used, and I utilize two mutual reactors y'Xz and 7'1/2X2 of the current-transformer type, one in the phase-A line-conductor and the other in the phase-C lineconductor. By way of example, a small resistor of 0.0086 X2 ohms is connected directly in series with the phase-C line-conductor, and shunted by a transformer Tlhaving a 1:100 ratio. As in Figs. 1 and 2, the secondary circuit of the voltageproducing network of Fig. 3 is so connected as to produce a positive-sequence delta-voltage which corresponds to Equation 13 in a system in Which [0:0 and R2=0.

In Fig. 4,- the voltage-producing network diers from the network shown in Fig. 1 in having two serially connected reactors 9`1/2X2, one traversed by Ia, and the other traversed by (Ia-i-Ic), the two reactors being serially included in the voltage-circuit 20, so that; their impedance-drops are added in the voltage-circuit.

Fig. 5 shows still another arrangement in which two 200-to-5-ratio current-transformers 2| and 22 are connected in the phase-C line-conductor C, and a 200-to-10-ratio current-transformer 23 is connected in the phase-A line-conductor A. The voltage-circuit 20 includes one resistor 0.866% and one reactor il/gXz. The currenttrans- :finer Zi circulates the current -Ic through the resistor 0.866552, and the two current-transformers 22 and 23, in parallel, circulate the current (2LH-Ic) through y'1/2X2, producing the voltages indicated in Equation 15.

In all of Figs. 1 to 5, and in the mathematical derivations, proper combinations of the deltacurrents of the line could have been utilized instead of star-currents, or a star-Voltage of the line could have been utilized instead of the delta- I voltage Eat, or the negative-sequence current could have been derived and passed directly through the negative-sequence impedance to produce the negative-sequence voltage-component Thus, if delta-currents were utilized, instead of star-currents, utilizing the transformation we could start with the equation for the negativesequence delta-current instead of Equation 6.

ySince the delta-phase line-currents Iab, Isc and Ice are, by definition, differential currents (Ia-Ib), etc., they have no zero-sequence component, or Isso, and We can eliminate any one of the delta-currents, from Equation 6* by using the equation To give only one illustration of one of the three preceding equations, in a system in which R2=0, We may rewrite Equation 13* as Fig. 6 shows a modification oi Fig. 5 in conforrnity with Equation 15*. The system shown in Fig. 6 uses three pairs of differentially connected current-transformers 24, 25 and 26 for deriving the delta line-currents Ica, lab and In), respectively, and a voltage-circuit 20* including two resistors 2'? and 28 of 0.289X2 ohms, and a reactor 29 of 0.5X2 ohms. The current-transformers 24 circulate the current -Iea through both of the resistors 21 and 2B; the current-transformers 25 circulate an additional current -Iab through one of the resistors, 28; and the current-transformers 26 circulate the current lab through the reactor 29, producing the voltagedrops called for in Equation 15*.

In like manner, star-voltages could be utiiized, instead of delta-voltages, provided that the zero-sequence component were absent from, or removed from, the star-voltages. The delta-voltage Eat in Equation 3 is a single phase of a threephase line-voltage having no zero-sequence voltage-component, so that said single phase is equal to the sum of the positive and negative-sequence components. The generality or this statement can be perceived from Equation 1, from which it is evident that the positive-sequence star-voltage component (or in general, the positive-sequcnce voltage, either star or delta) is E12 (Ea-E0) -E2 which corresponds to Equation 4.

Specifically considering the star voltages, or line-to-neutral voltages, E9., En, Ec, we have, therefore,

Choosing the last one, of the last six equations, for illustration, in a system in which Rzz, and deriving the delta-currents In) and Ita with diiierentially connected star-current transformers, so that the zero-sequence delta-current Inbo is eliminated, Equation l3* may he rewritten as (0.289X2-i-y'0.167X2) (Ib-Ie) (18) The conditions expressed in Equation i3 are fulfilled in the system shown in Fig. '2, wherein the star-connected secondary oi the power-transformer T is grounded at 3i, and the potentialtransformer PT is in the forni or a star-deltastar three-winding transformer-bank, with the delta-connected windings short-circuited, as indicated at 32, to eliminate the zero-sequence star-voltage component E0. Two pairs of diiierentially connected line-current transformers 34 and 35 produce the currents ZatzUa-Iw and Itc=(It-Ic), respectively. The current Ln; is circulated in an inductance 9@.333X2 in the secondary voltage-circuit 20", and the current 11m is circulated in an impedance (G.289X2|7',167X2), which is aiso connected in the voltage secondary circuit 2. The star voltage (Ea-E0) is derived from the potential transformer PT and connected in series with the impedances iBBBXg, 0.289Xz and 7'0,167X2 in the circuit 20, thus fulfilling the conditions of Equation 1S.

I have thus provided means, for deriving the positi voltage Een oi a three-phase iine, or for deriving the positive-sequence star-voltage quence line-impedance up to the point at which the voltage is to be determined. This is as expressed in Equation 5, with the star-delta current-transformations as dened by the equations IabIIa-Ib, IbeZIb-Ic and Ica=Ic-a. Th@ Ilegal tive-sequence current may be derived separately and passed through the negative-sequence impedance (R2-MK2), ork any equivalent combinations of currents may be substituted, as set forth in Equations 11,11', 11, 11*, 11*, or 113:". Thus I produce a positive-sequence voltage-response according to any one of a group of relationships expressed by Equations 12, 13, 13', 13, 13, 13*, 13*", 12, 13, 13', 13", 13*, 13*, and 13*".

My new positive-sequence voltage-deriving system may be called a compensator-system, as distinguished from a sequence-network vor other phase-sequence means, because my new system utilizes the compensator-method of modifying a potential-transformer voltage. Thus I add (or subtract) voltage-drops obtained by passing predetermined line-derived currents through predetermined impedances. In its broadest aspects, my invention contemplates any compensator-network which simulates tne negativesequence voltage-drop in the generator and in the line up to any given point, said negativesequence voltage-drop being subtracted from any line-voltage phase having no zero-sequence voltage-component, so as to produce a resultantvoltage equal to the positive-sequence component.

My invention is particularly useful in a voltage-regulator system of the type symbolically indicated in Fig. 8, the term voltage-regulator being utilized in the sense of a source of derived voltage, such as the voltage Esel, which energizes a variable load, which requires consideration of the variation of the derived voltage at the loadterrninals, when the load of the voltage-regulator varies between zero and full-load. Thus, in Fig. 8, a rst rectangle 4| indicates the potentialtransformer PTab or other source of derived linevoltage, a second rectangle 12 indicates the compensator-network, ample, to the secondary winding of the transformer Tr in Fig. 1 and the mutual-reactance secondary winding Ws, and a third rectangle d3 indicates a variable-load voltage-regulator network consisting of various variable shuntloads 44 and 45, connected by a serially connected impedance 46.

Calculations have shown that my compensatorsystem of positive-sequence voltage-derivation, as broadly symbolized in Fig. 8, is much more advantageous than any of the standard negativesequence voltage-networks, as it imposes a much smaller volt-ampere burden on the source il of line-derived voltage when supplying a heavy volt-ampere load at 43, and it 'also has a much better voltage-regulation between no load and full load on the output-terminals En of the positive-sequence voltage-segregating combination. I obtain these benets mainly by reason of the lower impedance of my compensator-network 42, for deriving the negative-sequence voltage, as compared to the impedance required in a conventional positive-sequence voltage-network utilizing voltages rather than currents.

Various modifications and special uses may be made of my system. Thus, the compensatornetwork 42 of Fig. 8, or the corresponding sources of the negative-sequence voltage Ene or E2 in Figs. 1 to '2, may be utilized alone, as a source of derived negative-sequence line-voltage, for energizing any device requiring a negativesequence voltage.

It is not always necessary or desirable to utilize very close approximations of the equivacorresponding, for ex` lent values of the negative-sequence resistancel R2 and reactance jXz of the line, up to the voltage-measuring point. By deliberately departing slightly from the absolutely correct values of the resistors and reactors utilized in the compensator-part of my positive-sequence voltagederiving means, I may obtain a voltage which is larger or smaller than the positive-sequence component Eem, by an increment or decrement depending upon the load on the generator G, thus providing cross-current compensation for parallel operation with other generators or regulatcrs (not shown). One means for accomplishing such a purpose is indicated in Fig. 1, wherein a resistance-changing tap 48 is provided on the resistor 0.866X2. Whenever I refer to values approximating the values necessary to obtain certain results, I contemplate such deliberate departures as have just been discussed.

In the foregoing derivations, I have utilized a single phase of a three-phase line-Voltage, and two phases of a three-phase line-current, with suitable impedances traversed by the two currentphases to produce a voltage-drop of substantially (R2-MK2) Iz. It is noted that these three-phase line-voltages or line-currents may be either starquantities or delta-quantities, each phase of the delta-quantities being dened as the difference between two star-quantities. Or a more complicated three-phase line-voltage or line-current may be utilized, each phase being made up of two (or more) delta or star phases of the line-voltage or current, vectorally combined in any manner and in any relative magnitudes, such, for example, as a set of three-phase line-quantities (voltage or current) made up as follows,

For phase-A, K QA-l-LQB-l-M Qc For phase-B, KQB-l-LQc-l-MQA For phase-C, KQc-l-LQA-l-MQB where QA, QB, Qc are the three-phase star or delta line-voltages or currents, and K, L and M are any constants or Vector-quantities. It is to be understood, of course, that the appropriate changes are to be made in the magnitudes and vector-relations of my compensator-impedances when such unusual transformations vare used.

I claim as my invention:

l. A positive-sequence voltage-deriving combination, comprising means for deriving a single phase of a three-phase line-voltage having no zero-sequence Voltage-component, means for causing line-current to pass through impedance in such manner as to produce a voltage-drop substantially corresponding to the negative-sequence line-voltage, and means for causing said voltagedrop to be subtracted from said single phase of the line-voltage to produce substantially the positive-sequence component ofthe line-voltage.

2. A positive-sequence voltage-deriving combination, comprising means for deriving a 4single phase of a three-phase line-voltage having no zero-sequence voltage-component, means for causing line-current to pass through impedance in such manner as to substantially produce the voltage-drop (R2-MK2) I2, where (Rz-l-jXz) is the negative-sequence impedance of the line up to the voltage-measuring point, and I2 is the negative-sequence component of the line-current, and means for causing said voltage-drop to be added to said single phase of the line-voltage to produce substantially the positive-sequence line-voltage.

3. A positive-sequence Voltage-deriving combination, comprising means for deriving a single phase of a three-phase line-voltage having no zero-sequence voltage-component, means for deriving two phases of a three-phase line-current having no zero-sequence current-component, means for causing said two phases of line-current to pass through impedances of such value as to substantially produce the voltage-drop (Rz-HXzUz, where (R2-MK2) is the negative sequence impedance of the line up to the voltagemeasuring point, and Iz is the negative-sequence component of the line-current, and means for causing said voltage-drop to be added to said single phase of the line-voltage to produce substantially the positive-sequence line-voltage.

4. A positive-sequence voltage-deriving combination, comprising means for deriving a single phase of a three-phase line-voltage having no zero-sequence voltage-component, and compensator-means for modifying the derived voltage, said compensator-means including impedance substantially corresponding to the negativesequence line-impedance, and means for causing line-current to traverse said impedance in such manner as to produce compensator-voltage substantially corresponding to the negative-sequence line-voltage, `characterized by said combination of derived line-voltage and compensator-voltage having substantially a relationship which is equivalent to the mathematical expression,

where the letters E and I represent line-voltages and line-currents, respectively, the subscript ab designates a delta-phase from which any zerosequence component has been removed, the subscripts 1 and 2 designate positive-sequence and negative-sequence components, respectively, and (Rz-MK2) is the negative-sequence impedan'ce of the line up to the voltage-measuring point.

5. A positive-sequence voltage-deriving combination, comprising means for deriving a single phase of a three-phase line-voltage having no zero-sequence voltage-component, means for deriving two phases of a threeephase line-current having no zero-sequence current-component, and compensator means for modifying the derived voltage, said compensator-means including impedances substantially corresponding to the negative-sequence line-impedance, and means for causing said two line-current phases to traverse said impedances in such manner as to produce compensator-voltage substantially corresponding to the negative-sequence line-voltage, characterized by said combination of derived line-voltage and compensator-Voltage having substantially a relationship which is equivalent to the mathematical expression,

Where the letters E and I represent line-voltages and line-currents, respectively, the subscripts a and c designate star-phases from which any zerosequence component has been removed, the subscripts l and 2 designate positive-sequence and negative-sequence components, respectively, and (RH-1X2) is the negative-sequence impedance of the line up to the voltage-measuring point.

6. A positive-sequence voltage-deriving combination, comprising means for deriving a single phase of a three-phase lineevoltage having no zero-sequence voltage-component, means for deriving two phases of a three-phase line-current having no zero-sequence current-component, and compensator-means for modifying the derived voltage, said compensator-means including impedances and means for causing said two linecurrent phases to traverse said impedances to produce compensator-voltage, characterized by said combination of derived line-voltage and compensator-voltage having substantially the relation,

where En) is the derived delta line-voltage, Is and Ie are the derived star line-currents, and (Rz-H'Xz) is the negative-sequence impedance of the line up to the voltagemeasuring point.

'7. A positive-sequence voltage-deriving comw bination, comprising means for deriving a single phase of a three-phase line-voltage having no zero-sequence voltage-component, means for deriving two phases of a three-phase 1inecurrent having no zero-sequence current-component, and compensator-means for modifying the derived voltage, said compensator-means including impedances and means for causing said two linecurrent phases to traverse said impedances to produce compensator-voltage, characterized by said combination of derived line-voltage and compensator-voltage having substantially the relation,

where En) is the 'derived delta line-voltage, Ib and Ic are the derived star line-currents, and (R2-MK2) is the negative-sequence impedance of the line up to the voltage-measuring point.

8. A positive-sequence voltage-deriving combination, comprising means for deriving a single phase of a three-phase line-voltage having no zero-sequence voltage-component, means for cleriving two phases of a three-phase line-current having no Zero-sequence current-component, and compensator-means for modifying the derived voltage, said compensator-means including impedances and means for causing said two linecurrent phases to traverse said impedances to produce compensator-voltage, characterized by said combination of derived line-voltage and compensator-voltage having substantially the relation,

Ea1=ab+ gvXH-aaningxz 12\/3R2 Ia++ 1/2\/3X21/2R2)I1 i 1/2X2+1/2v`3a2 1b where En is the derived delta line-voltage, Is and Ib are the derived star line-currents, and (R24-7X2) is the negative-sequence impedance of the line up to the voltage-measuring point.

9. Means for deriving the negative-sequence voltage-component from a three-phase line, com i phase line-current having no zero-sequence current-component, a plurality of serially connected impedances substantially corresponding to the negative-sequence line-impedance, and means for causing said two phases of line-current to pass through said impedances in such manner as to produce a total voltage-drop substantially corresponding to the negative-sequence linevoltage, the impedances and currents being of such values uo have substantially a relationship which is equivalent to the mathematical expression,

where the letters E and I represent line-voltages and line-currents, respectively, the subscripts a and c designate star-phases from which any Zero-sequence component has been removed, the subscript 2 designates the negative-sequence component, and (R24-7X2) is the negative-sequence impedance of the line up to the voltage measuring point.

11. Means for deriving the negative-sequence voltagewomponent from a three-phase line, Ing means for deriving two phases of a three-phase line-current having no zero-sequence current-component, a plurality of serially connected impedances, and means for causing said two phase-s of line-current to pass through said impedances, the impedances and currents being of such values as to have substantially the relation,

where Eabz is the derived negative-sequence delta line-voltage, I@ and Ie are the derived star linecurrents, and (Rz-i-XZ) is the negative-sequence impedance of the line to the voltage-measuring point.

12. Means for deriving the negative-sequence voltage-component from a three-phase line, comprising means for deriving two phases of a three-phase line-current having no zero-sequence current-component, a plurality of serially connected impedances, and means for causing said two phases of line-current to pass through said impede-ness, the impedances and currents being of such values as 'to have substantially the relation,

where Em is the derived negative-sequence delta line-voltage, Ib and I@ are the derived star linecurrents, and (R24-7X2) is the negative-sequence impedance of the line up to the voltage-measuring point.

13. Means for deriving the negative-sequence voltage-component from a three-phase line, comprising means for deriving two phases f a three-phase line-current having no zero-sequence current-component, a plurality of serially connected impedances, and means for causing said rtwo phases of line-current to pass through said impedances, the impedances and currents being of such values as to have substantially the relation,

where Em is the derived negative-sequence delta line-voltage, Ia and Ib are the derived star linecurrents, and (R24-7X2) is the negative-sequence impedance of the line up to the voltage-measuring point.

14. The positive-sequence voltage-deriving combination as defined in claim 1, in combination with a variable load-device therefor, requiring consideration of the variation of the derived positive-sequence voltage at the load-terminals, when said load varies.

15. The positive-sequence voltage-deriving combination as defined in claim 2, in combination with a variable load-device therefor, requiring consideration of the variation of the derived positive-sequence voltage at the load-terminals, when said load varies.

16. The positive-sequence voltage-deriving combination as dened in claim 3, in combination with a variable load-device therefor, requiring consideration of the variation of the derived positive-sequence Voltage at the load-terminals, when said load varies.

17. The positive-sequence voltage-deriving combination as defined in claim 4, in combination with a, variable load-device therefor, requiring consideration of the variation of the derived positive-sequence voltage at the load-terminals, when said load varies.

18. The positive-sequence voltage-deriving combination as defined in claim 5, in combination with a variable load-device therefor, requiring consideration of the variation of the derived positive-sequence voltage at the load-terminals, when said load varies.

19. The positive-sequence voltage-deriving combination a-s dened in claim 6, in combination with a variable load-device therefor, requiring consideration of the Variation of the derived positive-sequence voltage at the load-terminals, when said load varies.

20. The positive-sequence voltage-deriving combination as dened in claim 7, in combination with a variable load-device therefor, requiring consideration of the variation of the derived positive-sequence voltage at the load-terminals, when said load varies.

21. The positive-sequence voltage-deriving combination as defined in claim 8, in combination with a variable load-device therefor, requiring consideration of the variation of the derived The following references are of record in the le of this patent:

UNITED STATES PATENTS Name Date Freidlander June 19, 1934 Number 

